Proving groups are isomorphic

Recall that given a group G, we defined A(G) to be the set of all isomorphisms from G to itself; you proved that A(G) is a group under composition.
(a) Prove that A(Zn) is isomorphic to Zn/{0}
(b) Prove that A(Z) is isomorphic to Z2

Can you figure out the sets A(Zn) and A(Z)?
The identity function is one that should come to mind.
Take a general function on Z by f(x)=bx for some b in Z. What values can b take on so that f(x) is a bijection?